Thursday, January 7, 2016

The Golden Ratio

OK, I get it. It's been several months since I've posted and many of you suspect I've fallen off the face of the earth -- NOT! Many excuses surface in my mind but know this: I have not died nor have I become a zombie. I have been busy with my new solar panels building a 2.7kW system above our carport (believe me, this was a serious undertaking, not for the faint of heart). And now guess what: as our friend Arnold is fond of saying,  I'M BACK!

I have been fussing with that silly crossover point with my super tweeter and made good progress although I am still unhappy with the way it sounds. It is far better than it ever has been but you know how golden-ear types are: mercilessly critical. So the journey continues.

To refresh your memories, I use a Mundorf AMT for my tweter and a Bespoke Aria for my super tweeter. After countless attempts at a revised crossover point I have narrowed down the cause of the sibilance issue on the ST to a cavity resonance in  its enclosure. This combined with a mechanical resonance of the planar suspension of th ST at this same frequency proves to be a real nightmare.

At this point, I have been experimenting with series resonance filters (near 8KHz) to tame the wild beast and I have been marginally successful in doing so. But when I get the sibilance under control, the bass response goes out the window and vice versa. Now that the design has matured, I hear an occasional sporadic electrical resonance that is driving me literally bonkers. I tried not to redesign the enclosure (I like the way it looks) but alas, at this point I must yield to common sense.

So two things must be addressed: 1) the enclosure dimensions, and 2) the mechanical resonance of the diaphragm. Since this mechanical resonance is impacted by the enclosure resonance, it makes sense to redesign the enclosure first before tackling the mechanical issue.

Since their introduction in 1993, I have admired the design of the Bowers and Wilkins Nautilus speakers with their ground-braking logarithmic spiral woofer enclosure (also the Golden Ratio M,T,ST enclosures). For the Golden Ratio, the enclosure dimensions continuously converge in a1.618:1 ratio as shown below. BTW, the Nautilus speaker borrows its name from the sea creature whose shell also conforms to this same logarithmic spiral.

What interests me are the M-T-ST enclosures, what appears to be a unique tapered transmission line (TTL). Their super tweeter crosses at 3,500Hz. But the wavelength at 3500Hz is less than 4" so they must be using a multiple of that frequency (i.e., an inter-modular) for that enclosure. Interestingly, the model 804 uses a TTL enclosure for its ST of the 4" length.

So the next tale in the ongoing saga will be this new super-tweeter enclosure. I am uncertain as how I will go about this but old trumpets, horn flares, and waveguides come immediately to mind. We will see...

Yours for higher fidelity,

Philip Rastocny

I do not use ads in this blog to help support my efforts. If you like what you are reading, please remember to reciprocate by purchasing one of my eBooks or through a PayPal donation, My newest title is called Where, oh Where did the Star of Bethlehem Go? It’s an astronomer’s look at what this celestial object may have been, who the "Wise Men" were, and where they came from. Written in an investigative journalism style (like that of the Discovery Channel), it targets one star that has never been considered before and builds a solid case for its candidacy.

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